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<div class="moz-cite-prefix">Hi,</div>
<div class="moz-cite-prefix"><br>
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<div class="moz-cite-prefix">Peter G. Hinman: Recursion-Theoretic
Hierarchies might contain some related material.</div>
<div class="moz-cite-prefix"><br>
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<div class="moz-cite-prefix">Best, Till Mossakowski</div>
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<div class="moz-cite-prefix">Am 10.12.18 um 13:38 schrieb Siddharth
Bhat:<br>
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<blockquote type="cite"
cite="mid:CAPipc=1JnnuZupb9C8UD1Dmh3XoKumTuwLtJ8Z=ZBqGprg=g_Q@mail.gmail.com"><span>Hello,</span>
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</div>
<div>I was recently intrigued by this style of argument on haskell
cafe:</div>
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<div><br>
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<div>One can write a function <br>
Eq a => ((a -> Bool) -> a) -> [a]<br>
that enumerates the elements of the set. Because we have
universal quantification, this list can not be infinite. Which
makes sense, topologically: These so-called searchable sets are
topologically compact, and the Eq constraint means the space is
discrete. Compact subsets of a discrete space are finite. <br>
</div>
<div>-------</div>
<div><br>
</div>
<div>I've seen arguments like these "in the wild" during Scott
topology construction and in some other weird places
(hyperfunctions), but I've never seen a systematic treatment of
this.</div>
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<div><br>
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<div>I'd love to have a reference (papers / textbook preferred) to
self learn this stuff!</div>
<div><br>
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<div>Thanks</div>
<div>Siddharth</div>
-- <br>
<div dir="ltr" class="gmail_signature"
data-smartmail="gmail_signature">
<div dir="ltr">Sending this from my phone, please excuse any
typos!</div>
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<br>
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